Do you remember when President Jimmy Carter was attacked by a rabbit while fishing in 1979? Carter became the butt of many jokes about this incident. Here's a puzzle from John Tierney based on the incident:
What is your answer? The first correct answer wins a kiss from Alex.
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Suppose, the day after attacking President Carter, the rabbit finds itself alone in the middle of the pond, which is perfectly circular. Suppose there is a single Secret Service agent on the edge of the pond, armed with a small net to ensnare the swimming rabbit as it approaches the edge. This net is effective only if the rabbit is still in the water. If the rabbit reaches any point on the edge before the agent does, it can hop away to freedom; if the agent gets there first, the rabbit will be captured.
If the agent runs four times as fast as the rabbit swims, can the rabbit escape? If so, how?
For extra credit: What’s the fastest the agent can run (as a multiple of the rabbit’s speed) such that the rabbit can still escape?
What is your answer? The first correct answer wins a kiss from Alex.
Link via Instapundit
Comments (32)
So to beat the man, the rabbit needs to do more work than that. Kinda thinking a spiral pattern might work but I'm too lazy to do that math.
Let's try something simpler. If the rabbit can get himself sufficiently far in one direction, while forcing Secret Service man to be 180 degrees opposite, from there he clearly can win the race. If the pond has radius r, and the rabbit is x away from the center, then a straight swim to the edge is distance (r-x), in which time the man can run 4(r-x) and has to cover pi*r distance. So the rabbit has to be within pi*r/4 of the shore, or almost 1/4 of the way to the shore or closer, to win. The remaining question is can the rabbit get to that point, and force Secret Agent Man to the diametrically opposite side?
Well, rabbit swims 1/4 as fast as Man can run. So if rabbit is anywhere closer to the center than r/4, he can begin to swim in a circle and cover the angle faster than the man can run, and therefore swim in that circle until he forces man to be 180 degrees opposite. Then he can bolt for the shore, and to Rabbit Freedom.
So rabbit can swim to some point in between r/4 from the center and (1 - pi/4)r from the center. Regardless where the man is, Rabbi can then begin swimming his loop until the man is 180 opposite, then dash.
Ha!
"The rabbit would be able to swim from the center to the south edge in 2 seconds, while the agent would only be able to run from the north end to the south end in 3.14 seconds."
Actually the agent would be able to get from the north end to the south end in 1/2(pi) seconds; with a 2-meter radius, the pond's circumference is 4(pi), so half that is 2(pi). At 4 meters/second, 2(pi) meters would take about 1.57 seconds, and he would get there 0.43 seconds before the rabbit does.
http://www.neatorama.com/2008/12/10/green-exotic-women-vs-red-hot-men/
Queen Jealousy, envy waits behind him
Her fiery green gown sneers at the grassy ground
Blue are the life-giving waters taken for granted
They quietly understand
The once happy turquoise armies lay opposite ready
But wonder why the fight is on
My red is so confident, he flashes
Trophies of war and ribbons of euphoria
Orange is young, full of daring
But very unsteady for the first go round
My yellow in this case is not so mellow
In fact, I'm trying to say it's frightened like me
And all these emotions of mine keep holding me from
Giving my life to a rainbow like you
You have been eating bugs and didn't even know it.
Not to mention that the FDA and the Canadian Food administration don't make it mandatory for companies to list Cochineal as an in ingredient.
Mmmmnnn.